alexandria - Commonly Used Utilities

Version: 1.0.0
Licence: Public Domain / 0-clause MIT
Repository: alexandria/alexandria - Gitlab
See also: awesome-cl#language-extensions

This documentation is modified to markdown from here on 01 March, 2020.

In case of any inaccuracies, ambiguities or suggestions, please create an issue here.

---

ALEXANDRIA

Alexandria software and associated documentation are in the public domain:

Authors dedicate this work to public domain, for the benefit of the public at large and to the detriment of the authors' heirs and successors. Authors intends this dedication to be an overt act of relinquishment in perpetuity of all present and future rights under copyright law, whether vested or contingent, in the work. Authors understands that such relinquishment of all rights includes the relinquishment of all rights to enforce (by lawsuit or otherwise) those copyrights in the work.

Authors recognize that, once placed in the public domain, the work may be freely reproduced, distributed, transmitted, used, modified, built upon, or otherwise exploited by anyone for any purpose, commercial or non-commercial, and in any way, including by methods that have not yet been invented or conceived.

In those legislations where public domain dedications are not recognized or possible, Alexandria is distributed under the following terms and conditions:

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

---

1. HASH TABLES

ensure-gethash

Macro: (ensure-gethash key hash-table &optional default)

Like gethash, but if key is not found in the hash-table saves the default under key before returning it. Secondary return value is true if key was already in the table.

copy-hash-table

Function: (copy-hash-table table &key key test size rehash-size rehash-threshold)

Returns a copy of hash table table, with the same keys and values as the table. The copy has the same properties as the original, unless overridden by the keyword arguments.

Before each of the original values is set into the new hash-table, key is invoked on the value. As key defaults to cl:identity, a shallow copy is returned by default.

maphash-keys

Function: (maphash-keys function table)

Like maphash, but calls function with each key in the hash table table.

maphash-values

Function: (maphash-values function table)

Like maphash, but calls function with each value in the hash table table.

hash-table-keys

Function: (hash-table-keys table)

Returns a list containing the keys of hash table table.

hash-table-values

Function: (hash-table-values table)

Returns a list containing the values of hash table table.

hash-table-alist

Function: (hash-table-alist table)

Returns an association list containing the keys and values of hash table table.

hash-table-plist

Function: (hash-table-plist table)

Returns a property list containing the keys and values of hash table table.

alist-hash-table

Function: (alist-hash-table alist &rest hash-table-initargs)

Returns a hash table containing the keys and values of the association list alist. Hash table is initialized using the hash-table-initargs.

plist-hash-table

Function: (plist-hash-table plist &rest hash-table-initargs)

Returns a hash table containing the keys and values of the property list plist. Hash table is initialized using the hash-table-initargs.

---

2. DATA AND CONTROL FLOW

define-constant

Macro: (define-constant name initial-value &key test documentation)

Ensures that the global variable named by name is a constant with a value that is equal under test to the result of evaluating initial-value. test is a /function designator/ that defaults to eql. If documentation is given, it becomes the documentation string of the constant.

Signals an error if name is already a bound non-constant variable.

Signals an error if name is already a constant variable whose value is not equal under test to result of evaluating initial-value.

destructuring-case

Macro: (destructuring-case keyform &body clauses)

destructuring-case, -ccase, and -ecase are a combination of case and destructuring-bind. keyform must evaluate to a cons.

Clauses are of the form:

            ((CASE-KEYS . DESTRUCTURING-LAMBDA-LIST) FORM*)

The clause whose case-keys matches car of key, as if by case, ccase, or ecase, is selected, and FORMs are then executed with cdr of key is destructured and bound by the destructuring-lambda-list.

Example:

           (defun dcase (x)
             (destructuring-case x
               ((:foo a b)
                (format nil "foo: ~S, ~S" a b))
               ((:bar &key a b)
                (format nil "bar, ~S, ~S" a b))
               (((:alt1 :alt2) a)
                (format nil "alt: ~S" a))
               ((t &rest rest)
                (format nil "unknown: ~S" rest))))

            (dcase (list :foo 1 2))        ; ="foo: 1, 2"
            (dcase (list :bar :a 1 :b 2))  ; ="bar: 1, 2"
            (dcase (list :alt1 1))         ; ="alt: 1"
            (dcase (list :alt2 2))         ; ="alt: 2"
            (dcase (list :quux 1 2 3))     ; ="unknown: 1, 2, 3"

           (defun decase (x)
             (destructuring-case x
               ((:foo a b)
                (format nil "foo: ~S, ~S" a b))
               ((:bar &key a b)
                (format nil "bar, ~S, ~S" a b))
               (((:alt1 :alt2) a)
                (format nil "alt: ~S" a))))

            (decase (list :foo 1 2))        ; ="foo: 1, 2"
            (decase (list :bar :a 1 :b 2))  ; ="bar: 1, 2"
            (decase (list :alt1 1))         ; ="alt: 1"
            (decase (list :alt2 2))         ; ="alt: 2"
            (decase (list :quux 1 2 3))     ; =| error

ensure-functionf

Macro: (ensure-functionf &rest places)

Multiple-place modify macro for ensure-function: ensures that each of places contains a function.

multiple-value-prog2

Macro: (multiple-value-prog2 first-form second-form &body forms)

Evaluates first-form, then second-form, and then forms. Yields as its value all the value returned by second-form.

named-lambda

Macro: (named-lambda name lambda-list &body body)

Expands into a lambda-expression within whose body name denotes the corresponding function.

nth-value-or

Macro: (nth-value-or nth-value &body forms)

Evaluates form arguments one at a time, until the nth-value returned by one of the forms is true. It then returns all the values returned by evaluating that form. If none of the forms return a true nth value, this form returns nil.

if-let

Macro: (if-let bindings &body (then-form &optional else-form))

Creates new variable bindings, and conditionally executes either then-form or else-form. else-form defaults to nil.

bindings must be either single binding of the form:

           (variable initial-form)

or a list of bindings of the form:

           ((variable-1 initial-form-1)
            (variable-2 initial-form-2)
            ...
            (variable-n initial-form-n))

All initial-forms are executed sequentially in the specified order. Then all the variables are bound to the corresponding values.

If all variables were bound to true values, the then-form is executed with the bindings in effect, otherwise the else-form is executed with the bindings in effect.

when-let

Macro: (when-let bindings &body forms)

Creates new variable bindings, and conditionally executes forms.

bindings must be either single binding of the form:

           (variable initial-form)

or a list of bindings of the form:

           ((variable-1 initial-form-1)
            (variable-2 initial-form-2)
            ...
            (variable-n initial-form-n))

All initial-forms are executed sequentially in the specified order. Then all the variables are bound to the corresponding values.

If all variables were bound to true values, then forms are executed as an implicit progn.

Macro: (when-let* bindings &body forms)

Creates new variable bindings, and conditionally executes forms.

bindings must be either single binding of the form:

           (variable initial-form)

or a list of bindings of the form:

           ((variable-1 initial-form-1)
            (variable-2 initial-form-2)
            ...
            (variable-n initial-form-n))

Each initial-form is executed in turn, and the variable bound to the corresponding value. Initial-form expressions can refer to variables previously bound by the when-let*.

Execution of when-let* stops immediately if any initial-form evaluates to nil. If all initial-forms evaluate to true, then forms are executed as an implicit progn.

switch

Macro: (switch whole (object &key test key) &body clauses)

Evaluates first matching clause, returning its values, or evaluates and returns the values of default if no keys match.

cswitch

Macro: (cswitch whole (object &key test key) &body clauses)

Like switch, but signals a continuable error if no key matches.

eswitch

Macro: (eswitch whole (object &key test key) &body clauses)

Like switch, but signals an error if no key matches.

whichever

Macro: (whichever &rest possibilities env)

Evaluates exactly one of possibilities, chosen at random.

xor

Macro: (xor &rest datums)

Evaluates its arguments one at a time, from left to right. If more then one argument evaluates to a true value no further datums are evaluated, and nil is returned as both primary and secondary value. If exactly one argument evaluates to true, its value is returned as the primary value after all the arguments have been evaluated, and t is returned as the secondary value. If no arguments evaluate to true nil is retuned as primary, and t as secondary value.

disjoin

Function: (disjoin predicate &rest more-predicates)

Returns a function that applies each of predicate and more-predicate functions in turn to its arguments, returning the primary value of the first predicate that returns true, without calling the remaining predicates. If none of the predicates returns true, nil is returned.

conjoin

Function: (conjoin predicate &rest more-predicates)

Returns a function that applies each of predicate and more-predicate functions in turn to its arguments, returning nil if any of the predicates returns false, without calling the remaining predicates. If none of the predicates returns false, returns the primary value of the last predicate.

compose

Function: (compose function &rest more-functions)

Returns a function composed of function and more-functions that applies its arguments to to each in turn, starting from the rightmost of more-functions, and then calling the next one with the primary value of the last.

Function: (ensure-function function-designator)

Returns the function designated by function-designator: if function-designator is a function, it is returned, otherwise it must be a function name and its fdefinition is returned.

multiple-value-compose

Function: (multiple-value-compose function &rest more-functions)

Returns a function composed of function and more-functions that applies its arguments to each in turn, starting from the rightmost of more-functions, and then calling the next one with all the return values of the last.

curry

Function: (curry function &rest arguments)

Returns a function that applies arguments and the arguments it is called with to function.

rcurry

Function: (rcurry function &rest arguments)

Returns a function that applies the arguments it is called with and arguments to function.

---

3. CONSES

proper-list

Type designator for proper lists. Implemented as a satisfies type, hence not recommended for performance intensive use. Main usefullness as a type designator of the expected type in a type-error.

circular-list

Type designator for circular lists. Implemented as a satisfies type, so not recommended for performance intensive use. Main usefullness as the expected-type designator of a type-error.

appendf

Macro: (appendf place &rest lists env)

Modify-macro for append. Appends lists to the place designated by the first argument.

nconcf

Macro: (nconcf place &rest lists env)

Modify-macro for nconc. Concatenates lists to place designated by the first argument.

remove-from-plistf

Macro: (remove-from-plistf place &rest keys env)

Modify macro for remove-from-plist.

delete-from-plistf

Macro: (delete-from-plistf place &rest keys env)

Modify macro for delete-from-plist.

reversef

Macro: (reversef place env)

Modify-macro for reverse. Copies and reverses the list stored in the given place and saves back the result into the place.

nreversef

Macro: (nreversef place env)

Modify-macro for nreverse. Reverses the list stored in the given place by destructively modifying it and saves back the result into the place.

unionf

Macro: (unionf place list &rest args env)

Modify-macro for union. Saves the union of list and the contents of the place designated by the first argument to the designated place.

nunionf

Macro: (nunionf place list &rest args env)

Modify-macro for nunion. Saves the union of list and the contents of the place designated by the first argument to the designated place. May modify either argument.

doplist

Macro: (doplist (key val plist &optional values) &body body)

Iterates over elements of plist. body can be preceded by declarations, and is like a tagbody. return may be used to terminate the iteration early. If return is not used, returns values.

circular-list-p

Function: (circular-list-p object)

Returns true if object is a circular list, nil otherwise.

circular-tree-p

Function: (circular-tree-p object)

Returns true if object is a circular tree, nil otherwise.

proper-list-p

Function: (proper-list-p object)

Returns true if object is a proper list.

alist-plist

Function: (alist-plist alist)

Returns a property list containing the same keys and values as the association list alist in the same order.

plist-alist

Function: (plist-alist plist)

Returns an association list containing the same keys and values as the property list plist in the same order.

circular-list

Function: (circular-list &rest elements)

Creates a circular list of elements.

make-circular-list

Function: (make-circular-list length &key initial-element)

Creates a circular list of length with the given initial-element.

ensure-car

Function: (ensure-car thing)

If thing is a cons, its car is returned. Otherwise thing is returned.

ensure-cons

Function: (ensure-cons cons)

If cons is a cons, it is returned. Otherwise returns a fresh cons with cons in the car, and nil in the cdr.

ensure-list

Function: (ensure-list list)

If list is a list, it is returned. Otherwise returns the list designated by list.

flatten

Function: (flatten tree)

Traverses the tree in order, collecting non-null leaves into a list.

lastcar

Function: (lastcar list)

Returns the last element of list. Signals a type-error if list is not a proper list.

(setf

Function: ((setf lastcar))

Sets the last element of list. Signals a type-error if list is not a proper list.

proper-list-length

Function: (proper-list-length list)

Returns length of list, signalling an error if it is not a proper list.

mappend

Function: (mappend function &rest lists)

Applies function to respective element(s) of each list, appending all the all the result list to a single list. function must return a list.

map-product

Function: (map-product function list &rest more-lists)

Returns a list containing the results of calling function with one argument from list, and one from each of more-lists for each combination of arguments. In other words, returns the product of list and more-lists using function.

Example:

           (map-product 'list '(1 2) '(3 4) '(5 6))
            =((1 3 5) (1 3 6) (1 4 5) (1 4 6)
                (2 3 5) (2 3 6) (2 4 5) (2 4 6))

remove-from-plist

Function: (remove-from-plist plist &rest keys)

Returns a propery-list with same keys and values as plist, except that keys in the list designated by keys and values corresponding to them are removed. The returned property-list may share structure with the plist, but plist is not destructively modified. Keys are compared using eq.

delete-from-plist

Function: (delete-from-plist plist &rest keys)

Just like remove-from-plist, but this version may destructively modify the provided plist.

set-equal

Function: (set-equal list1 list2 &key test key)

Returns true if every element of list1 matches some element of list2 and every element of list2 matches some element of list1. Otherwise returns false.

setp

Function: (setp object &key test key)

Returns true if object is a list that denotes a set, nil otherwise. A list denotes a set if each element of the list is unique under key and test.

---

4. SEQUENCES

proper-sequence

Type designator for proper sequences, that is proper lists and sequences that are not lists.

deletef

Macro: (deletef place item &rest remove-keywords env)

Modify-macro for delete. Sets place designated by the first argument to the result of calling delete with item, place, and the remove-keywords.

removef

Macro: (removef place item &rest remove-keywords env)

Modify-macro for remove. Sets place designated by the first argument to the result of calling remove with item, place, and the remove-keywords.

rotate

Function: (rotate sequence &optional n)

Returns a sequence of the same type as sequence, with the elements of sequence rotated by n: n elements are moved from the end of the sequence to the front if n is positive, and -n elements moved from the front to the end if n is negative. sequence must be a proper sequence. n must be an integer, defaulting to 1.

If absolute value of n is greater then the length of the sequence, the results are identical to calling rotate with

            (* (signum n) (mod n (length sequence))).

Note: the original sequence may be destructively altered, and result sequence may share structure with it.

shuffle

Function: (shuffle sequence &key start end)

Returns a random permutation of sequence bounded by start and end. Original sequece may be destructively modified, and share storage with the original one. Signals an error if sequence is not a proper sequence.

random-elt

Function: (random-elt sequence &key start end)

Returns a random element from sequence bounded by start and end. Signals an error if the sequence is not a proper non-empty sequence, or if end and start are not proper bounding index designators for sequence.

emptyp

Function: (emptyp sequence)

Returns true if sequence is an empty sequence. Signals an error if sequence is not a sequence.

sequence-of-length-p

Function: (sequence-of-length-p sequence length)

Return true if sequence is a sequence of length length. Signals an error if sequence is not a sequence. Returns false for circular lists.

length=

Function: (length= &rest sequences)

Takes any number of sequences or integers in any order. Returns true iff the length of all the sequences and the integers are equal. Hint: there's a compiler macro that expands into more efficient code if the first argument is a literal integer.

copy-sequence

Function: (copy-sequence type sequence)

Returns a fresh sequence of type, which has the same elements as sequence.

first-elt

Function: (first-elt sequence)

Returns the first element of sequence. Signals a type-error if sequence is not a sequence, or is an empty sequence.

(setf first-elt)

Function: ((setf first-elt))

Sets the first element of sequence. Signals a type-error if sequence is not a sequence, is an empty sequence, or if object cannot be stored in sequence.

last-elt

Function: (last-elt sequence)

Returns the last element of sequence. Signals a type-error if sequence is not a proper sequence, or is an empty sequence.

(setf last-elt)

Function: ((setf last-elt))

Sets the last element of sequence. Signals a type-error if sequence is not a proper sequence, is an empty sequence, or if object cannot be stored in sequence.

starts-with

Function: (starts-with object sequence &key test key)

Returns true if sequence is a sequence whose first element is eql to object. Returns nil if the sequence is not a sequence or is an empty sequence.

starts-with-subseq

Function: (starts-with-subseq prefix sequence &rest args &key return-suffix &allow-other-keys)

Test whether the first elements of sequence are the same (as per TEST) as the elements of prefix.

If return-suffix is t the functions returns, as a second value, a displaced array pointing to the sequence after prefix.

ends-with

Function: (ends-with object sequence &key test key)

Returns true if sequence is a sequence whose last element is eql to object. Returns nil if the sequence is not a sequence or is an empty sequence. Signals an error if sequence is an improper list.

ends-with-subseq

Function: (ends-with-subseq suffix sequence &key test)

Test whether sequence ends with suffix. In other words: return true if the last (length SUFFIX) elements of sequence are equal to suffix.

map-combinations

Function: (map-combinations function sequence &key start end length copy)

Calls function with each combination of length constructable from the elements of the subsequence of sequence delimited by start and end. start defaults to 0, end to length of sequence, and length to the length of the delimited subsequence. (So unless length is specified there is only a single combination, which has the same elements as the delimited subsequence.) If copy is true (the default) each combination is freshly allocated. If copy is false all combinations are eq to each other, in which case consequences are specified if a combination is modified by function.

map-derangements

Function: (map-derangements function sequence &key start end copy)

Calls function with each derangement of the subsequence of sequence denoted by the bounding index designators start and end. Derangement is a permutation of the sequence where no element remains in place. sequence is not modified, but individual derangements are eq to each other. Consequences are unspecified if calling function modifies either the derangement or sequence.

map-permutations

Function: (map-permutations function sequence &key start end length copy)

Calls function with each permutation of length constructable from the subsequence of sequence delimited by start and end. start defaults to 0, end to length of the sequence, and length to the length of the delimited subsequence.

5. IO

---

read-file-into-string

Function: (read-file-into-string pathname &key buffer-size external-format)

Return the contents of the file denoted by pathname as a fresh string.

The external-format parameter will be passed directly to with-open-file unless it's nil, which means the system default.

Function: (read-file-into-byte-vector pathname)

Read pathname into a freshly allocated (unsigned-byte 8) vector.

---

6. MACRO WRITING

once-only

Macro: (once-only specs &body forms)

Evaluates forms with symbols specified in specs rebound to temporary variables, ensuring that each initform is evaluated only once.

Each of specs must either be a symbol naming the variable to be rebound, or of the form:

            (symbol initform)

Bare symbols in specs are equivalent to

            (symbol symbol)

Example:

            (defmacro cons1 (x) (once-only (x) `(cons ,x ,x)))
            (let ((y 0)) (cons1 (incf y))) =(1 . 1)

with-gensyms

Macro: (with-gensyms names &body forms)

Binds each variable named by a symbol in names to a unique symbol around forms. Each of names must either be either a symbol, or of the form:

           (symbol string-designator)

Bare symbols appearing in names are equivalent to:

           (symbol symbol)

The string-designator is used as the argument to gensym when constructing the unique symbol the named variable will be bound to.

with-unique-names

Macro: (with-unique-names names &body forms)

Alias for with-gensyms.

featurep

Function: (featurep feature-expression)

Returns t if the argument matches the state of the *features* list and nil if it does not. feature-expression can be any atom or list acceptable to the reader macros #+ and #-.

parse-body

Function: (parse-body body &key documentation whole)

Parses body into (values remaining-forms declarations doc-string). Documentation strings are recognized only if documentation is true. Syntax errors in body are signalled and whole is used in the signal arguments when given.

parse-ordinary-lambda-list

Function: (parse-ordinary-lambda-list lambda-list 
             &key normalize 
                  allow-specializers 
                  normalize-optional
                  normalize-keyword
                  normalize-auxilary)

Parses an ordinary lambda-list, returning as multiple values:

1. Required parameters.

2. Optional parameter specifications, normalized into form:

             (name init suppliedp)

3. Name of the rest parameter, or nil.

4. Keyword parameter specifications, normalized into form:

             ((keyword-name name) init suppliedp)

5. Boolean indicating &allow-other-keys presence.

6. &aux parameter specifications, normalized into form

             (name init).

Signals a program-error is the lambda-list is malformed.

---

7. SYMBOLS

ensure-symbol

Function: (ensure-symbol name &optional package)

Returns a symbol with name designated by name, accessible in package designated by package. If symbol is not already accessible in package, it is interned there. Returns a secondary value reflecting the status of the symbol in the package, which matches the secondary return value of intern.

Example:

            (ensure-symbol :cons :cl) =cl:cons, :external

format-symbol

Function: (format-symbol package control &rest arguments)

Constructs a string by applying arguments to string designator control as if by format within with-standard-io-syntax, and then creates a symbol named by that string.

If package is nil, returns an uninterned symbol, if package is t, returns a symbol interned in the current package, and otherwise returns a symbol interned in the package designated by package.

make-keyword

Function: (make-keyword name)

Interns the string designated by name in the keyword package.

make-gensym

Function: (make-gensym name)

If name is a non-negative integer, calls gensym using it. Otherwise name must be a string designator, in which case calls gensym using the designated string as the argument.

make-gensym-list

Function: (make-gensym-list length &optional x)

Returns a list of length gensyms, each generated as if with a call to make-gensym, using the second (optional, defaulting to "G") argument.

symbolicate

Function: (symbolicate &rest things)

Concatenate together the names of some strings and symbols, producing a symbol in the current package.

---

8. ARRAYS

array-index

Type designator for an index into array of
`length:` an integer between `0` (inclusive) and `length` (exclusive).
`length` defaults to `array-dimension-limit`.



### array-length

Type designator for a dimension of an array of length: an integer between 0 (inclusive) and length (inclusive). length defaults to array-dimension-limit.

copy-array

Function: (copy-array array &key element-type fill-pointer
adjustable)

Returns an undisplaced copy of array, with same fill-pointer and adjustability (if any) as the original, unless overridden by the keyword arguments.

---

9. TYPES

string-designator

A string designator type. A string designator is either a string, a symbol, or a character.

coercef

Macro: (coercef place type-spec env)

Modify-macro for coerce.

of-type

Function: (of-type type)

Returns a function of one argument, which returns true when its argument is of type.

type=

Function: (type= type1 type2)

Returns a primary value of t is type1 and type2 are the same type, and a secondary value that is true is the type equality could be reliably determined: primary value of nil and secondary value of t indicates that the types are not equivalent.

---

10. NUMBERS

maxf

Macro: (maxf place &rest numbers env)

Modify-macro for max. Sets place designated by the first argument to the maximum of its original value and numbers.

minf

Macro: (minf place &rest numbers env)

Modify-macro for min. Sets place designated by the first argument to the minimum of its original value and numbers.

binomial-coefficient

Function: (binomial-coefficient n k)

Binomial coefficient of n and k, also expressed as n choose k. This is the number of k element combinations given n choises. n must be equal to or greater then k.

count-permutations

Function: (count-permutations n &optional k)

Number of k element permutations for a sequence of n objects. k defaults to n

clamp

Function: (clamp number min max)

Clamps the number into [min, max] range. Returns min if number is lesser then min and max if number is greater then max, otherwise returns number.

lerp

Function: (lerp v a b)

Returns the result of linear interpolation between A and b, using the interpolation coefficient v.

factorial

Function: (factorial n)

Factorial of non-negative integer n.

subfactorial

Function: (subfactorial n)

Subfactorial of the non-negative integer n.

gaussian-random

Function: (gaussian-random &optional min max)

Returns two gaussian random double floats as the primary and secondary value, optionally constrained by min and max. Gaussian random numbers form a standard normal distribution around 0.0d0.

Sufficiently positive min or negative max will cause the algorithm used to take a very long time. If min is positive it should be close to zero, and similarly if max is negative it should be close to zero.

iota

Function: (iota n &key start step)

Return a list of n numbers, starting from start (with numeric contagion from step applied), each consequtive number being the sum of the previous one and step. start defaults to 0 and step to 1.

Examples:

            (iota 4)                      =(0 1 2 3)
            (iota 3 :start 1 :step 1.0)   =(1.0 2.0 3.0)
            (iota 3 :start -1 :step -1/2) =(-1 -3/2 -2)

map-iota

Function: (map-iota function n &key start
step)

Calls function with n numbers, starting from start (with numeric contagion from step applied), each consequtive number being the sum of the previous one and step. start defaults to 0 and step to 1. Returns n.

Examples:

            (map-iota #'print 3 :start 1 :step 1.0) =3
              ;;; 1.0
              ;;; 2.0
              ;;; 3.0

mean

Function: (mean sample)

Returns the mean of sample. sample must be a sequence of numbers.

median

Function: (median sample)

Returns median of sample. sample must be a sequence of real numbers.

variance

Function: (variance sample &key biased)

Variance of sample. Returns the biased variance if biased is true (the default), and the unbiased estimator of variance if biased is false. sample must be a sequence of numbers.

standard-deviation

Function: (standard-deviation sample &key biased)

Standard deviation of sample. Returns the biased standard deviation if biased is true (the default), and the square root of the unbiased estimator for variance if biased is false (which is not the same as the unbiased estimator for standard deviation). sample must be a sequence of numbers.